First- and second-order phase transitions in Ising models on small world networks, simulations and comparison with an effective field theory

TL;DR

This paper investigates phase transitions in Ising models on small-world networks through simulations and compares the results with an effective field theory, revealing complex critical behavior and stability issues.

Contribution

It provides a comprehensive simulation study validating an effective field theory for Ising models on small-world networks, including analysis of phase transition types and stability.

Findings

Confirmation of multicritical points with first- or second-order transitions

Validation of theoretical predictions for critical surfaces and correlations

Discovery of instability in the Edwards-Anderson model with d_0=2

Abstract

We perform simulations of random Ising models defined over small-world networks and we check the validity and the level of approximation of a recently proposed effective field theory. Simulations confirm a rich scenario with the presence of multicritical points with first- or second-order phase transitions. In particular, for second-order phase transitions, independent of the dimension d_0 of the underlying lattice, the exact predictions of the theory in the paramagnetic regions, such as the location of critical surfaces and correlation functions, are verified. Quite interestingly, we verify that the Edwards-Anderson model with d_0=2 is not thermodynamically stable under graph noise.